[Opinions] Re: Does this nickname work? + a combo question
Ellie as a nickname for Madeline works technically, but it seems awfully contrived. You'd forever be explaining how you came up with Ellie as a nickname for Madeline. Addie is also a possibility, as is Adele.
Also, just some food for thought... Mädchen is the German word for 'girl', but also in German, pet forms of names are created by taking the root of a name and adding '-chen' (meaning 'little') to the end. For example, Gretchen means 'little Greta' or 'little Margretha/Margrethe'. If you really wanted to get creative with a nickname, Mädchen could possibly work for Madeline, using 'Mad-' (plus the umlaut) and '-chen'. It would be a double entendre of sorts.
As for the combo, I like Alice Katharina Hermione. I think it has the better flow and works better than Alice Hermione Katharina. Katharina seems like a forceful, dominant name, so it needs something light like Hermione to finish out the combo.